Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$ How we can make Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$? What can be S in $Cay(D_{2n},S)$ and $ Cay(\mathbb Z_n ,S)$, Please write one example. Thanks for advise.--prophetes.ai

Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$ How we can make Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$? What can be S in $Cay(D_{2n},S)$ and $ Cay(\mathbb Z_n ,S)$, Please write one example. Thanks for advise.

Here's an example of a Cayley graph for the group $\mathbb{Z}_{10}$:

![A Cayley graph for $\\mathbb{Z}_{10}$](

The vertices are the underlying set of the group $\mathbb{Z}_{10}$, and we draw edges between $g$ and $g+h$ whenever $g,h \in S$ where $S=\\{\pm 1, \pm 2\\}$.

Here's an example of a Cayley graph for the dihedral group $D_{10}$:

![A Cayley graph for $D_{10}$](

The vertices are the underlying set of the dihedral group with presentation $$D=\langle f,r | f^2=e, r^5=e, rf=fr^{-1} \rangle,$$ (we can think of $f$ as "flip" and $r$ as "rotation") and we draw edges between $g$ and $g+h$ whenever $g,h \in S$ where $S=\\{f,r,r^{-1}\\}$.